Problem 14 · 2024 Math Kangaroo
Hard
Spatial & Visual Reasoning
spatial-reasoning
Which two of the shapes shown on the right can you put together to form a cuboid?
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Answer: B — 2 and 3
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Hint 1 of 3
A cuboid is a full rectangular block with flat faces and no notches; first count the unit cubes in each piece.
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Hint 2 of 3
The two pieces you join must total the cube count of a neat block (like 2×2×2 or 2×2×3), and their bumps and dents must fill each other exactly.
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Hint 3 of 3
Look for the pair whose stair-step notch on one piece is filled by the matching bump on the other.
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Approach: find the pair whose notch and bump complete a flat rectangular block
- Each pictured piece is a small cluster of unit cubes with a step or notch, so a single piece is not yet a full block.
- Two pieces form a cuboid only when one piece's notch is exactly filled by the other's protruding cubes, leaving flat faces all around.
- Testing the offered pairs, pieces 2 and 3 interlock with no gaps or overhangs into a solid block.
- The answer is 2 and 3.
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